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Wewaii [24]
2 years ago
6

Write an equation for the line that passes through (- 3, 5) and is parallel to y = - 6x + 1.

Mathematics
1 answer:
soldier1979 [14.2K]2 years ago
3 0

Answer:

y-5 = -6(x+3) OR y = -6x-13

Step-by-step explanation:

Let's use slope-intercept form to solve this problem.

Slope intercept form is the following:

y-y1 = m(x-x1)

x1 and y1 are given by the point in the problem.

x1 = -3, y1 = 5.

m is given by the equation in the problem. Lines that are parallel have the same slope. Thus,

m = -6.

If we plug these values into the equation for slope intercept form, we get the following:

y-5 = -6(x-(-3)) which becomes y-5 = -6(x+3)

This is an acceptable answer to the problem. However, point-slope form is also a way it can be written.

y-5 = -6x-18

y = -6x-13

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The scale factor for a model is 5cm= m model: 9.5cm actual : 30.5m
MaRussiya [10]

We are given dimensions of model and actual figure.

model: 9.5cm actual : 30.5m.

We need to find the length of actual shape for the scale factor 5cm.

Let us assume actual length be x m.

Let us set a proportion now.

<h3>5 : x = 9.5 : 30.5</h3>

Let us convert proportion into fractions.

\frac{5}{x}=\frac{9.5}{30.5}

On cross multiplying, we get

9.5x = 5× 30.5

9.5x = 152.5.

On dividing both sides by 9.5, we get

\frac{9.5x}{9.5}=\frac{152.5}{9.5}

x=16.05.

<h3>Therefore, the scale factor for a model is 5cm= 16.05 m.</h3>

6 0
3 years ago
Find the slope of a line passing through the given points. 2,5) and (4,-7) help me
LekaFEV [45]

<em>-7 -5 / 4 -2 / -12/2 </em>

<em>-12/2 = -6 </em>

<em>Slope: -6x </em>

<em>5 = 2(-6) + b</em>

<em>5 = -12 + b </em>

<em>-12 + 17 = 5 </em>

<em>Slope intercept Form: y = -6x + 17</em>

7 0
3 years ago
Jerry needs 216 posts to build a fence. He has 88 posts and needs P more. Write an equation that you could use to find the numbe
devlian [24]

Answer:

P = 128 Post

Step-by-step explanation:

Total post needed = 216 posts

Number of post Jerry has = 88 posts

Number of posts jerry still needs = P

Total = Number of post Jerry has + Number of posts jerry still needs

216 = 88 + P

216 - 88 = P

128 = P

P = 128 Post

7 0
3 years ago
An amortized loan of RM60,000 has annual payments for fifteen years, the first occurring exactly one year after the loan is made
Nimfa-mama [501]

9514 1404 393

Answer:

  a) RM2256.09 . . . principal paid by 8th payment

  b) RM1791.10 . . . . interest paid by 12th payment

Step-by-step explanation:

First of all, we need to find the payments.

The payment amount is the amount that makes the future value of the series of payments equal to the future value of the loan at the given interest rate.

The future value of a single amount is ...

  FV = P(1 +r)^n . . . . . where r is the annual rate, and n is the number of years in the future

The future value of a series of payments is ...

  FV = P((1 +r)^n -1)/r . . . . . where n is the number of payments of P earning annual rate r

For payments in a series that does not end at the end of the loan, the future value is the product of that of the series and the effect of the accumulation of interest for the remaining time.

__

The first 4 payments will have a future value at the end of the loan period of ...

  s1 = X((1 +0.05)^4 -1)/0.05×(1 +0.05)^11 = X(1.05^15 -1.05^11)/0.05

  s1 = 7.3717764259X

The next 5 payments will have a future value at the end of the loan period of ...

  s2 = 2X((1 +0.05)^5 -1)/0.05×(1 +0.05)^6 = 2X(1.05^11 -1.05^6)/0.05

  s2 = 14.8097486997X

The last 6 payments will have a future value at the end of the loan period of ...

  s3 = 4X((1 +0.05)^6 -1)/0.05 = 27.20765125X

So, the total future value of the series of payments is ...

  payment value = 7.3717764259X +14.8097486997X +27.20765125X

  = 49.3891763756X

__

The future value of the loan amount after 15 years is ...

  loan value = 60,000(1 +0.05)^15 = 124,735.69

In order for these amounts to be the same, we must have ...

  49.3891763756X = 124,735.69

  X = 124,735.69/49.3891763756 = 2,525.57

__

At this point, it is convenient to use a spreadsheet to find the interest and principal portions of each of the loan payments. (We find the interest charge to be greater than the payment amount for the first 4 payments. So, the loan balance is increasing during those years.)

In the attached, we have shown the interest on the beginning balance, and the principal that changes the beginning balance to the ending balance after each payment. (That is, the interest portion of the payment is on the row above the payment number.)

The spreadsheet tells us ...

A) the principal repaid in the 8th payment is RM2,256.09

B) the interest paid in the 12th payment is RM1,791.10

_____

<em>Additional comment</em>

The spreadsheet "goal seek" function could be used to find the payment amount that makes the loan balance zero at the end of the term.

We have used rounding to sen (RM0.01) in the calculation of interest payments. The effect of that is that the "goal seek" solution is a payment value of 2525.56707 instead of the 2525.56734 that we calculated above. The value rounded to RM0.01 is the same in each case: 2525.57.

3 0
2 years ago
4564644*4434688=124x^2
Anna [14]

Answer:

Step-by-step explanation:Let's solve your equation step-by-step.

(4564644)(4434688)=124x2

Step 1: Simplify both sides of the equation.

20242771971072=124x2

Step 2: Subtract 124x^2 from both sides.

20242771971072−124x2=124x2−124x2

−124x2+20242771971072=0

Step 3: Subtract 20242771971072 from both sides.

−124x2+20242771971072−20242771971072=0−20242771971072

−124x2=−20242771971072

Step 4: Divide both sides by -124.

−124x2

−124

=

−20242771971072

−124

x2=

5060692992768

31

Step 5: Take square root.

x=±√

5060692992768

31

x=404039.801328,−404039.801328

Answer:

x=404039.801328,−404039.801328

3 0
2 years ago
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